Friday, February 17, 2012

The Length of our Day is getting Longer -- Really

Day length, or length of day refers to the time each day from the moment the upper curve of the sun's disk appears above the horizon during sunrise to the moment when it disappears below the horizon during sunset.

We all realize that the length of the day changes with season. In the norther hemisphere, the shortest day of the year is around December 21st on the Winter solstice and the longest day is June 21st on the summer solstice.

But other than seasonal differences, day length is actually increasing because the Earth rotation is slowing has been for the past 4.5 billion years. Why? It is because of the Moon. Since the Moon's mass is a fraction of that of the Earth (about 1:81), the two bodies interact as a double planet system, rather than as a planet with a satellite. The plane of the Moon's orbit around the Earth lies close to the plane of the Earth's orbit around the Sun. The mass of the Moon is sufficiently large, and it is sufficiently close, to raise tides in the oceans of Earth.

However, the rotation drags the position of the tidal bulge ahead of the position directly under the Moon. As a consequence, there exists a substantial amount of mass in the bulge that is offset from the line through the centers of the Earth and Moon. Because of this offset, a portion of the gravitational pull between Earth's tidal bulges and the Moon is perpendicular to the Earth-Moon line, i.e. there exists a torque between the Earth and the Moon. This boosts the Moon in its orbit (moving it away from the Earth), and decelerates the rotation of the Earth.

As a result of this process, the length of our day, which is nominally 86400 seconds long, is actually getting longer. The small difference accumulates every day, which leads to an increasing difference between our clock time (Universal Time) on the one hand, and Atomic Time on the other hand. This makes it necessary to insert a leap second every once in a while.

Scientists have measured these changes in day length by using the geologic record. Sedimentary deposits can be studied because they show alternating layers of sand and silt laid down offshore from estuaries with tidal flows. Daily, monthly and seasonal cycles can be found in the deposits. Similar patterns can be seen as well in the growth of coral (including fossil coral), that have fluctuations based on tides. Here is a picture showing sedimentary and coral fluctuations.

In the future, tidal acceleration would continue until the rotational period of the Earth matched the orbital period of the Moon. At that time, the Moon would always be overhead of a single fixed place on Earth. Such a situation already exists in the Pluto-Charon system. However, the slowdown of the Earth's rotation is not occurring fast enough for the rotation to lengthen to a month before other effects make this irrelevant: About 2.1 billion years from now, the continual increase of the Sun's radiation will cause the Earth's oceans to vaporize, removing the bulk of the tidal friction and acceleration.

These sedimentary and coral growth measurements, along with other paleontological evidence, have allowed scientists to model the changes in earth rotation speed, number of days in the year, and moon to earth distance. As for the latter figures, scientists think that the earth was only 12,000 miles away after the moon was first formed around 4.5 billion years ago when a Mars-sized planet struck the earth. Today the moon is 238,857 miles away (384,403 km).

From the observed change in the Moon's orbit, the corresponding change in the length of the day can be computed to be around +2.3 ms per century. The moon is also moving away from the earth around two inches (5 cm) per year. As the Moon creeps further away it carries energy away with it. This loss of energy manifests itself by the slowing of our planet.

I was curious what data I could find to substantiate the premise that the moon's movement away from the earth has changed the length of an Earth day as well as the number of days in a year. I found a technical paper that had the data:  

Here are the charts I created from the data.

The bottom axis in both charts corresponds in time from the present to 4,500 million years ago (left to right).   Scientists think that 4.5 billion years ago the length of an Earth day was only 6.1 hours.  The shorter day length required 1,434 days for the Earth to make a complete revolution of the Sun.

1 comment:

  1. But on the shorter time scales sometimes the crust of the earth rotates faster and makes the days shorter than they were. See the plots at
    and note in particular that 100 years ago the earth took 3 ms longer to rotate once than it does today. It just happens that 1912 was the year of the slowest rotation in recorded history.